Vettel, who started from the pit lane and set the fastest lap of the race, now has 255 points to Alonso's 245 and can clinch a third successive title in Austin, Texas, in two weeks if results go his way.
"It was an unbelievable day for Sebastian today," said Red Bull team principal Christian Horner after Vettel also had to pit for a new front wing in the early stages.
Red Bull could have clinched the constructors' championship for the third year in a row on Sunday but were made to wait after Australian Mark Webber crashed out. They now have 422 points to Ferrari's 340 with 86 remaining to be won.
Vettel and Alonso are the only drivers still in contention for the title, with Raikkonen third overall but 57 behind Red Bull's 25-year-old German.
In Image: Second place Ferrari driver Fernando Alonso of Spain steers his car during the Emirates Formula One Grand Prix